Multiscale spectral analysis for detecting short and long range change points in time series

Abstract

Identifying short and long range change points in an observed time series that consists of stationary segments is a common problem. These change points mark the time boundaries of the segments where the time series leaves one stationary state and enters another. Due to certain technical advantages, analysis is carried out in the frequency domain to identify such change points in the time domain. What is considered as a change may depend on the time scale. The results of the analysis are displayed in the form of graphs that display change points on different time horizons (time scales), which are observed to be statistically significant. The methodology is illustrated using several simulated and real time series data. The method works well to detect change points and illustrates the importance of analysing the time series on different time horizons.